Exploring lower peak sidelobe windows with the same mainlobe as rectangular window via nature-inspired methodology

Symmetrical windows are widely used as smoothing weighting for signals undergoing discrete Fourier transform (DFT) processing. Briefly speaking, the resolution of spectral analysis is governed by mainlobe width (MW) of a window, and the variance estimates are decreased by the sidelobes leakage with the window. It is generally believed that there has an optimal trade-off between MW and sidelobes ripple levels. The rectangular window (RW) has the smallest MW, but with the highest peak-sidelobe ratio (PSLR). The lower sidelobes of nonrectangular windows, however, have been achieved at the cost of the MW broadening. This paper poses a challenging question of whether the PSLR of a window can be reduced while, preserving the same MW as RW. To demystify this question, we present a global optimization procedure, firefly algorithm (FA), borrowed from nature-inspired methodology, to compute the proposed optimization formulation and perform an extensive number of experimental tests. The experimental results show that the PSLRs of optimized windows can be reduced by 0.98–4.04 dB, while preserving the same MW as RW. Furthermore, adjusting the parameters of optimization algorithm, we find that the lower PSLR of optimized window generally leads to higher envelope level of the sidelobes ripple.